一维Frenkel-Kontorova模型原子链的同宿轨和拟周期行为研究  

Study ofhomoclinic orbits and quasi-period behavior of atomic chain in the one-dimensional Frenkel-Kontorova model

作　　者：康举 黄头生 孟天祥 张化永[1] KANG Ju;HUANG Tou-sheng;MENG Tian-xiang;ZHANG Hua-yong(Research Center for Engineering Ecology and Nonlinear Science,North China Electric Power University,Beijing 102206,China)

机构地区：[1]华北电力大学工程生态学与非线性科学研究中心,北京102206

出　　处：《大学物理》2018年第12期26-29,共4页College Physics

基　　金：水体污染控制与治理科技重大专项(2017ZX07101-002);中央高校基本科研业务费专项资金(JB2017069);国家自然科学基金(39560023)资助

摘　　要：基于一维Frenkel-Kontorova模型,研究了原子链系统的同宿轨道、多周期振荡和拟周期振荡的动力学行为.首先,根据Jacobian矩阵的特征值判断了系统存在双曲型鞍焦点;其次,运用Silnikov定理判定了系统在鞍焦点处产生同宿轨道的条件;最后,通过数值模拟验证了系统存在同宿轨道、多周期振荡和拟周期振荡的动力学行为.本文的研究结果也为固体摩擦现象的研究提供了一个有价值的参考.The dynamic behaviors of homoclinic orbits,multi-period oscillation and quasi-period oscillation of an atomic chain are investigated by the one-dimensional Frenkel-Kontorova model.Firstly,the hyperbolic saddle focus existed in the system is decided by the eigenvalues of Jacobian matrix.Secondly,the condition of system generation homoclinic orbits is determined via Silnikov theorem at the hyperbolic saddle focus.Finally,the numerical simulation is used to verify the existence of homoclinic orbits,multi-period oscillation and quasi-period oscillation of the system.The results of this paper also provide a valuable reference for the study of solid friction phenomena.

关 键 词：一维Frenkel—Kontorova模型 同宿轨道 多周期振荡 拟周期振荡 双曲型鞍焦点 

分 类 号：O562.4[理学—原子与分子物理]